To get to St Paul from the UT campus you can take the Red River/Cameron road shuttle from 2525 San Jacinto (just south of Dean Keaton) to Harris Dr and Red River. St Paul will be 500 feet (152 meters) north of the bus stop. The UT shuttle buses run only when UT is in session. The Capitol Metro web page has the timetable for the Red River/Cameron Road shuttle and the shuttle bus schedule for each semester.
The Capitol Metro Trip Planner can assist you in finding bus information.